Complex Langevin simulation of a random matrix model at nonzero chemical potential
Abstract In this paper we test the complex Langevin algorithm for numerical simulations of a random matrix model of QCD with a first order phase transition to a phase of finite baryon density. We observe that a naive implementation of the algorithm leads to phase quenched results, which were also de...
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2018-03-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP03(2018)015 |
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doaj-art-805c0b801ded49639ed8965c44f448e02018-08-15T21:57:56ZengSpringerJournal of High Energy Physics1029-84792018-03-012018313310.1007/JHEP03(2018)015Complex Langevin simulation of a random matrix model at nonzero chemical potentialJ. Bloch0J. Glesaaen1J. J. M. Verbaarschot2S. Zafeiropoulos3Institute for Theoretical Physics, University of RegensburgDepartment of Physics, Swansea UniversityDepartment of Physics and Astronomy, Stony Brook UniversityInstitute for Theoretical Physics, Heidelberg UniversityAbstract In this paper we test the complex Langevin algorithm for numerical simulations of a random matrix model of QCD with a first order phase transition to a phase of finite baryon density. We observe that a naive implementation of the algorithm leads to phase quenched results, which were also derived analytically in this article. We test several fixes for the convergence issues of the algorithm, in particular the method of gauge cooling, the shifted representation, the deformation technique and reweighted complex Langevin, but only the latter method reproduces the correct analytical results in the region where the quark mass is inside the domain of the eigenvalues. In order to shed more light on the issues of the methods we also apply them to a similar random matrix model with a milder sign problem and no phase transition, and in that case gauge cooling solves the convergence problems as was shown before in the literature.http://link.springer.com/article/10.1007/JHEP03(2018)015Lattice QCDLattice Quantum Field TheoryMatrix Models |
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| language |
English |
| format |
Article |
| author |
J. Bloch J. Glesaaen J. J. M. Verbaarschot S. Zafeiropoulos |
| spellingShingle |
J. Bloch J. Glesaaen J. J. M. Verbaarschot S. Zafeiropoulos Complex Langevin simulation of a random matrix model at nonzero chemical potential Journal of High Energy Physics Lattice QCD Lattice Quantum Field Theory Matrix Models |
| author_facet |
J. Bloch J. Glesaaen J. J. M. Verbaarschot S. Zafeiropoulos |
| author_sort |
J. Bloch |
| title |
Complex Langevin simulation of a random matrix model at nonzero chemical potential |
| title_short |
Complex Langevin simulation of a random matrix model at nonzero chemical potential |
| title_full |
Complex Langevin simulation of a random matrix model at nonzero chemical potential |
| title_fullStr |
Complex Langevin simulation of a random matrix model at nonzero chemical potential |
| title_full_unstemmed |
Complex Langevin simulation of a random matrix model at nonzero chemical potential |
| title_sort |
complex langevin simulation of a random matrix model at nonzero chemical potential |
| publisher |
Springer |
| series |
Journal of High Energy Physics |
| issn |
1029-8479 |
| publishDate |
2018-03-01 |
| description |
Abstract In this paper we test the complex Langevin algorithm for numerical simulations of a random matrix model of QCD with a first order phase transition to a phase of finite baryon density. We observe that a naive implementation of the algorithm leads to phase quenched results, which were also derived analytically in this article. We test several fixes for the convergence issues of the algorithm, in particular the method of gauge cooling, the shifted representation, the deformation technique and reweighted complex Langevin, but only the latter method reproduces the correct analytical results in the region where the quark mass is inside the domain of the eigenvalues. In order to shed more light on the issues of the methods we also apply them to a similar random matrix model with a milder sign problem and no phase transition, and in that case gauge cooling solves the convergence problems as was shown before in the literature. |
| topic |
Lattice QCD Lattice Quantum Field Theory Matrix Models |
| url |
http://link.springer.com/article/10.1007/JHEP03(2018)015 |
| _version_ |
1612704800907984896 |